Accuracy synthesis of a multi-level hybrid positioning mechanism for the feed support system in FAST

• Error due to time-varying barycenter is modeled, and compensation strategy is given.
• Error model for multi-level hybrid mechanism is deduced with clear physical meaning.
• Efficient approach to acquire hybrid mechanism׳s error boundary is first proposed.
• Accuracy synthesis method for hybrid mechanism is given.
• Adding measure system helps balance weight and accuracy and satisfy accuracy index.

This study examines the terminal accuracy synthesis of a multi-level hybrid positioning mechanism for the feed support system in a Five-hundred-meter Aperture Spherical Radio Telescope (FAST) project, specifically considering three types of error influence factors such as time-varying barycenter, geometric error, and structural deformation. An error model caused by a time-varying barycenter and that for the entire mechanism are first established, and the physical meaning of the latter is further explained. The three factors that influence terminal accuracy are then analyzed. An efficient approach for acquiring the terminal error boundary over the entire workspace is proposed on the basis of the vector set theory and a linear algebra method. After employing an error compensation method for the first-level mechanism through control strategy, terminal accuracy synthesis is conducted by using a nonlinear optimization algorithm. Both constraints for accuracy and weight are satisfied after introducing measurement systems. Moreover, the proposed method of accuracy analysis and synthesis can be applied to other multi-level hybrid mechanisms.